First thought: You sound like you're a good developer, which is a great foundation in this situation because people feel that we have a broad understanding of technology -- and they're right! You're correct in your insecurity though - a good developer is not exactly what they're after.
They want a solution, and if you can become the guy who knows how to navigate all the complexities involved in delivering that solution... Well, then you're the guy. And you're much more valuable.
And you don't have to stop coding, either. Which has always been my phobia.
So that's more or less how I present myself to my clients. I'm a developer, but I'm also a competent project manager. I know how to take your project from here to done even though it may involve designers, IT guys, additional developers, datacenters, etc.
Working with other professionals: You probably aren't in a position to hire folks. That's fine, but find good partners, and you can market your self as a shop or consulting group that is good at more than one thing. Believe me, people will appreciate that! For instance, we have a fantastic partner in Romania that we use for a lot of design, and we add value because we know how to get results from them and handle all the communication and so on. My customers don't want to talk to 3 to 6 people, they want a single point of contact who is accountable for all of it.
One thought here: try to find people who do this full time. Moonlighters and people doing side jobs have constantly let me down. I sympathize; I know what it's like to be spread too thin.
Fixed prices: You will probably have to deal with fixed prices, and you will need to hold your partners to fixed prices (or have some other mechanismf or controlling costs) if that's the case. Once the relationship becomes more comfortable, I usually try to give clients a range of what I think a job will take -- 5 to 8 hours, etc. And I let them know that fixed prices are a little bad for them because I have to assume some risk, which means they get charged more.
Most companies still want actual fixed prices for larger projects though and many large companies are shockingly comfortable with being overcharged in this situation. Fixed prices seems to be unfortunate fact of life in the contract development space.